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Index B


B-key

B

b-key

b

BachBound

BachBound(K) : FldNum -> RngIntElt

backspace-key

<Backspace>

BadPrimes

BadPrimes(E) : CurveEll -> [ RngIntElt ]

baer

Plane_baer (Example H57E14)

Ball

Ball(u, n) : GrphVert, RngIntElt -> { GrphVert }

Ball(u, n) : Vert, RngIntElt -> { GrphVert }

Bang

Coercion(D, C) : Struct, Struct -> Map

Base

Base(G) : GrpMat -> [Elt]

Base(G) : GrpPerm -> [Elt]

base

Base and Strong Generator Functions (MATRIX GROUPS)

Base and Strong Generator Functions (PERMUTATION GROUPS)

BaseExtend

BaseExtend(E, K, h) : CurveEll, Rng, Map -> CurveEll

Elcu_BaseExtend (Example H53E3)

BaseField

CoefficientField(V) : ModTupFld -> Fld

BaseImage

BaseImage(x) : GrpPermElt -> [Elt]

BaseModule

BaseModule(R, S) : AlgMat, Rng -> ModTup

BasePoint

BasePoint(G, i) : GrpMat, RngIntElt -> Elt

BasePoint(G, i) : GrpPerm, RngIntElt -> Elt

BaseRing

BaseRing(R) : AlgMat -> Rng

BaseRing(F) : FldFun -> Rng

BaseRing(L) : Lat -> Rng

BaseRing(P) : RngMPol -> Rng

BaseRing(O) : RngOrd -> Rng

BaseRing(R) : RngSer -> Rng

BaseRing(P) : RngUPol -> Rng

CoefficentRing(M) : ModMPol -> ModMPol

CoefficientRing(A) : AlgGen -> Rng

CoefficientRing(G) : GrpMat -> Rng

CoefficientRing(M) : ModTupRng -> Rng

Bases

FldNum_Bases (Example H36E9)

bases

Bases (ALGEBRAS)

Bases (MATRIX ALGEBRAS)

basic

Basic Small Group Functions (GROUPS)

basic-trngps

Basic Small Group Functions (GROUPS)

BasicAccess

GrpPerm_BasicAccess (Example H20E9)

BasicOrbit

BasicOrbit(G, i) : GrpMat, RngIntElt -> SetIndx

BasicOrbit(G, i) : GrpPerm, RngIntElt -> SetIndx

BasicOrbitLength

BasicOrbitLength(G, i) : GrpMat, RngIntElt -> RngIntElt

BasicOrbitLength(G, i) : GrpPerm, RngIntElt -> RngIntElt

BasicOrbitLengths

BasicOrbitLengths(G) : GrpMat -> [RngIntElt]

BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]

BasicOrbits

BasicOrbits(G) : GrpPerm -> [SetIndx]

BasicStabiliser

BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat

BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm

BasicStabiliserChain

BasicStabilizerChain(G) : GrpMat -> [GrpMat]

BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]

BasicStabilizer

BasicStabilizer(G, i) : GrpMat, RngIntElt -> GrpMat

BasicStabilizer(G, i) : GrpPerm, RngIntElt -> GrpPerm

BasicStabilizerChain

BasicStabilizerChain(G) : GrpMat -> [GrpMat]

BasicStabilizerChain(G) : GrpPerm -> [GrpPerm]

Basis

Basis(A) : AlgGen -> [ AlgGenElt ]

Basis(R) : AlgMat -> [ AlgMatElt ]

Basis(C) : Code -> [ ModTupFldElt ]

Basis(L) : Lat -> [ FldReElt ]

Basis(M) : ModMPol -> RngMPolElt

Basis(V) : ModTupFld -> [ModTupFldElt]

Basis(M) : ModTupRng -> [ModTupRngElt]

Basis(I) : RngFunOrdIdl -> [FldFunElt]

Basis(I) : RngMPol -> RngMPolElt

Basis(O) : RngOrd -> [ FldNumElt ]

Basis(I) : RngOrdIdl -> [RngOrdElt]

Basis(O) : RngQuad -> [ FldQuadElt ]

CharacterTable(G) : Grp -> SeqEnum

KMod_Basis (Example H41E12)

basis

Bases (VECTOR SPACES)

Bases for Free Modules (GENERAL MODULES)

Basis (QUADRATIC FIELDS)

Basis Representation (FUNCTION FIELDS AND THEIR ORDERS)

Basis Representation (NUMBER FIELDS AND THEIR ORDERS)

Basis Representation (NUMBER FIELDS AND THEIR ORDERS)

Ideal Bases (MULTIVARIATE POLYNOMIAL RINGS)

Module Bases (MODULES OVER AFFINE ALGEBRAS)

BasisElement

BasisElement(A, i) : AlgGen, RngIntElt -> AlgGenElt

BasisElement(R, i) : AlgMat, RngIntElt -> AlgMatElt

BasisElement(M, i) : ModMPol, RngIntElt -> RngMPolElt

BasisElement(V, i) : ModTupFld, RngIntElt -> ModTupFldElt

BasisElement(M, i) : ModTupRng, RngIntElt -> ModTupRngElt

BasisElement(I, i) : RngMPol, RngIntElt -> RngMPolElt

BasisMatrix

BasisMatrix(S) : AlgGrpSub -> ModMatRngElt

BasisMatrix(C) : Code -> ModMatFldElt

BasisMatrix(L) : Lat -> ModMatRngElt

BasisMatrix(M) : ModMPol -> ModMatRngElt

BasisMatrix(V) : ModTupFld -> ModMatElt

BasisMatrix(M) : ModTupRng -> ModMatElt

BasisMatrix(I) : RngFunOrdIdl -> AlgMatElt

BasisMatrix(O) : RngOrd -> AlgMatElt

BasisMatrix(I) : RngOrdIdl -> AlgMatElt

BasisProduct

BasisProduct(A, i, j) : AlgGen, RngIntElt, RngIntElt -> AlgGenElt

BasisProducts

BasisProducts(A) : AlgGen -> [[ AlgGenElt ]]

BasisValues

BasisValues(O) : RngFunOrd -> SeqEnum, RngIntElt, RngIntElt, RngIntElt

BCH

Construction of BCH Codes and their Generalizations (ERROR-CORRECTING CODES)

BCHCode

BCHCode(K, n, d, b) : FldFin, RngIntElt, RngIntElt, RngIntElt -> Code

Code_BCHCode (Example H58E8)

begin

Overview (OVERVIEW)

BernoulliApproximation

BernoulliApproximation(n) : RngIntElt -> FldPrElt

BernoulliApproximation(n) : RngIntElt -> FldPrElt

BernoulliNumber

BernoulliNumber(n) : RngIntElt -> FldRatElt

BernoulliNumber(n) : RngIntElt -> RngIntElt

BernoulliPolynomial

BernoulliPolynomial(n) : RngIntElt -> RngUPolElt

bessel

Gamma, Bessel and Associated Functions (REAL AND COMPLEX FIELDS)

BesselFunction

BesselFunction(n, r) : RngIntElt, FldReElt -> FldReElt

BestApproximation

BestApproximation(r, n) : FldPrElt, RngIntElt -> FldPrElt

BetterPoly

FldNum_BetterPoly (Example H36E4)

BetterPolynomial

BetterPolynomial(K) : FldNum -> BoolElt, FldNum

BFSTree

BreadthFirstSearchTree(u) : GrphVert -> Grph

bibliography

Bibliography for Database of Groups of Order Dividing 256 (OVERVIEW)

Bibliography for Database of Groups of Order Dividing 729 (OVERVIEW)

Bibliography for Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)

Bibliography for Database of Simple Groups (OVERVIEW)

Bicomponents

Bicomponents(G) : GrphUnd -> [GrphUnd]

bigger

Comparison (OVERVIEW)

BigO

BigO(x^n) : RngElt -> RngIntElt

BigO(x^n) : RngSerElt -> RngIntElt

binary

Binary Set Operators (SETS)

binding

Key Bindings (Emacs and VI mode) (ENVIRONMENT AND OPTIONS)

Key Bindings in Emacs mode only (ENVIRONMENT AND OPTIONS)

Key Bindings in VI mode only (ENVIRONMENT AND OPTIONS)

Binomial

Binomial(n, r) : RngIntElt, RngIntElt -> RngIntElt

Binomial(n, r) : RngIntElt, RngIntElt -> RngIntElt

bInvariants

bInvariants(E) : CurveEll -> [ RngElt ]

BipartiteGraph

BipartiteGraph(m, n) : RngIntElt, RngIntElt -> GrphUnd

Bipartition

Bipartition(G) : GrphUnd -> [ { GrphVert } ]

BiquadraticResidueSymbol

BiquadraticResidueSymbol(a, b) : FldQuadElt, FldQuadElt -> FldQuadElt

BKABdsInfoRate

BKABdsInfoRate(K, delta) : FldFin, FldPrElt -> FldPrElt, FldPrElt

BKBdsCardLargestCode

BKBdsCardLargestCode(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt, RngIntElt

BKBdsCardLargestLinearCode

BKBdsCardLargestLinearCode(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt, RngIntElt

BKBdsMaxMinimumWeight

BKBdsMaxMinimumWeight(K, n, k) : FldFin, RngIntElt, RngIntElt -> RngIntElt, RngIntElt

blackbox

BLACKBOX GROUPS

Groups (OVERVIEW)

BlackboxGroup

BlackboxGroup(n) : RngIntElt -> GrpBB

GrpBB_BlackboxGroup (Example H17E1)

Block

Block(D, i) : Inc, RngIntElt -> IncBlk

Line(D, p, q) : Inc, IncPt, IncPt -> IncBlk

block

Creating Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)

Operations on Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)

The Point-Set and Block-Set of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)

BlockDegree

BlockDegree(D) : Dsgn -> RngIntElt

BlockDegree(D, B) : Inc, IncBlk -> RngIntElt

BlockDegrees

BlockDegrees(D) : Inc -> [ RngIntElt ]

BlockGraph

BlockGraph(D) : Inc -> Grph

BlockGraph(D) : Inc -> GrphUnd

BlockGroup

BlockGroup(D) : Inc -> GrpPerm

Blocks

Blocks(D) : Inc -> { IncBlk }

BlocksAction

BlocksAction(G, P) : GrpPerm, GSet -> Hom(GrpPerm), GrpPerm, GrpPerm

BlocksActions

GrpPerm_BlocksActions (Example H20E15)

BlockSet

BlockSet(D) : Inc -> IncBlkSet

BlocksImage

BlocksImage(G) : GrpMat -> GrpPerm

BlocksImage(G, P) : GrpPerm, GSet -> GrpPerm

BlockSize

BlockDegree(D) : Dsgn -> RngIntElt

BlockDegree(D, B) : Inc, IncBlk -> RngIntElt

BlockSizes

BlockDegrees(D) : Inc -> [ RngIntElt ]

BlocksKernel

BlocksKernel(G, P) : GrpPerm, GSet -> GrpPerm

BlockSystem

BlockSystem(G) : GrpMat -> Rec

book

Documentation (OVERVIEW)

Boolean

Boolean Functions (INPUT AND OUTPUT)

Boolean Functions and Operators (SETS)

Boolean Operators for Elements (FINITELY PRESENTED ALGEBRAS)

Boolean Operators on Ideals (INTRODUCTION [RINGS AND FIELDS])

Boolean Predicates (ERROR-CORRECTING CODES)

Booleans (OVERVIEW)

Comparison of Words (FINITELY PRESENTED GROUPS)

Comparison Operators for Elements (SOLUBLE GROUPS)

Elementary Graph Predicates (GRAPHS)

Equality (TUPLES AND CARTESIAN PRODUCTS)

Equality and Comparison (ABELIAN GROUPS)

Equality and Comparison (BLACKBOX GROUPS)

Equality and Comparison (FINITELY PRESENTED SEMIGROUPS)

Equality and Membership (FINITE FIELDS)

Equality and Membership (INTRODUCTION [RINGS AND FIELDS])

Equality and Membership (RATIONAL FIELD)

Equality and Membership (RESIDUE CLASS RINGS)

Equality and Membership (RING OF INTEGERS)

General Group Properties (ABELIAN GROUPS)

General Group Properties (SOLUBLE GROUPS)

General Properties of Subgroups (ABELIAN GROUPS)

General Properties of Subgroups (SOLUBLE GROUPS)

Generic Predicates (LOCAL FIELDS)

Membership and Equality (ABELIAN GROUPS)

Membership and Equality (BLACKBOX GROUPS)

Membership and Equality (GENERAL MODULES)

Membership and Equality (GROUPS)

Membership and Equality (MATRIX ALGEBRAS)

Membership and Equality (MATRIX GROUPS)

Membership and Equality (PERMUTATION GROUPS)

Membership and Equality (SOLUBLE GROUPS)

Membership and Equality (VECTOR SPACES)

Predicates (MATRIX ALGEBRAS)

Predicates and Boolean Operators (ELLIPTIC CURVES)

Predicates and Boolean Operators (QUADRATIC FIELDS)

Predicates and Booleans (CHARACTERS OF FINITE GROUPS)

Predicates for Matrices (MATRIX GROUPS)

Predicates on Ideals (FUNCTION FIELDS AND THEIR ORDERS)

Predicates on Ideals (NUMBER FIELDS AND THEIR ORDERS)

Predicates on Ring Elements (CYCLOTOMIC FIELDS)

Predicates on Ring Elements (FINITE FIELDS)

Predicates on Ring Elements (INTRODUCTION [RINGS AND FIELDS])

Predicates on Ring Elements (MULTIVARIATE POLYNOMIAL RINGS)

Predicates on Ring Elements (POWER SERIES AND LAURENT SERIES)

Predicates on Ring Elements (RATIONAL FIELD)

Predicates on Ring Elements (RATIONAL FUNCTION FIELDS)

Predicates on Ring Elements (RESIDUE CLASS RINGS)

Predicates on Ring Elements (RING OF INTEGERS)

Predicates on Ring Elements (UNIVARIATE POLYNOMIAL RINGS)

Predicates on Sequences (SEQUENCES)

Properties of a Matrix Group (MATRIX GROUPS)

Properties of a Module (GENERAL MODULES)

Properties of a Permutation Group (PERMUTATION GROUPS)

Properties of Subgroups (FINITELY PRESENTED GROUPS)

Ring Predicates (NUMBER FIELDS AND THEIR ORDERS)

Ring Predicates and Booleans (RATIONAL FIELD)

Ring Predicates and Booleans (REAL AND COMPLEX FIELDS)

Ring Predicates and Booleans (RING OF INTEGERS)

boolean

Boolean values (STATEMENTS AND EXPRESSIONS)

Predicates on Elements (FUNCTION FIELDS AND THEIR ORDERS)

Predicates on Elements (NUMBER FIELDS AND THEIR ORDERS)

Predicates on Points (ELLIPTIC CURVES)

Properties of Incidence Structures and Designs (INCIDENCE STRUCTURES AND DESIGNS)

Properties of Planes (FINITE PLANES)

Ring Predicates and Booleans (CYCLOTOMIC FIELDS)

Ring Predicates and Booleans (MULTIVARIATE POLYNOMIAL RINGS)

Ring Predicates and Booleans (POWER SERIES AND LAURENT SERIES)

Ring Predicates and Booleans (UNIVARIATE POLYNOMIAL RINGS)

Boolean-generic

Generic Predicates (LOCAL FIELDS)

Booleans

Booleans() : Nil -> Bool

State_Booleans (Example H1E8)

Bottom

Bottom(L): SubGrpLat -> SubGrpLatElt

Bottom(L): SubModLat -> SubModLatElt

bound

Bounds (ERROR-CORRECTING CODES)

Lower Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

Upper Asymptotic Bounds on the Information Rate (ERROR-CORRECTING CODES)

Upper Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

brace

Sets (OVERVIEW)

bracestar\starbrace

{* *} : Null -> SetMulti

bracket

Expression (OVERVIEW)

Generator Assignment (OVERVIEW)

Sequences (OVERVIEW)

Sets (OVERVIEW)

BravaisGroup

BravaisGroup(G) : GrpMat -> GrpMat

BreadthFirstSearchTree

BreadthFirstSearchTree(u) : GrphVert -> Grph

break

Early Exit from Iterative Statements (STATEMENTS AND EXPRESSIONS)

The break statement (OVERVIEW)

State_break (Example H1E15)

BSGS

Base and Strong Generator Functions (MATRIX GROUPS)

Base and Strong Generator Functions (PERMUTATION GROUPS)

BSGS(G) : GrpMat ->

BSGS(G) : GrpPerm ->

GrpPerm_BSGS (Example H20E23)

BSGS-base-strong-generator

Base and Strong Generator Functions (MATRIX GROUPS)

Base and Strong Generator Functions (PERMUTATION GROUPS)

Bstar

Bstar(a) : RngFunOrdElt -> FldRatElt

bug

Magma Updates (OVERVIEW)

BuildSchreierVector

[Future release] BuildSchreierVector(G, i) : GrpPerm, RngIntElt ->

BuildSubgroups

GrpFP_BuildSubgroups (Example H16E20)

builtin

Intrinsics (OVERVIEW)

by

Call by Value Evaluation (MAGMA SEMANTICS)

Expression (OVERVIEW)

Sequences (OVERVIEW)

Sets (OVERVIEW)

The for statement (OVERVIEW)

bye

Control-C key (OVERVIEW)

Quitting (OVERVIEW)


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